Trellis encoding technique for PCM modems

ABSTRACT

A method of applying a multidimensional error reduction/correction algorithm on a stream of one dimensional symbols, comprising converting the stream of one dimensional symbols into a corresponding stream of two dimensional symbols; and, applying the multidimensional error reduction/correction algorithm to the stream of two dimensional symbols. The invention also provides a method of normalizing a metric used by an error reduction/correction algorithm on a stream of symbols wherein the symbols are non-uniformly spaced, comprising: determining a minimum distance (dmin) between two closest symbols in the stream, for each symbol in the stream, determining a minimum distance (dsym) between each symbol in the stream and each of its adjacent neighboring symbols, and, normalizing the metric used by the error reduction/correction algorithm by the ratio dmin/dsym.

[0001] Applicant hereby claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application Serial No. 60/049,107, filed Jun. 9, 1997. This application is a continuation of U.S. Application Ser. No. 09/093,704, filed Jun. 9, 1998, the entirety of which is incorporated herein by reference.

FIELD OF THE INVENTION

[0002] This invention relates generally to a trellis encoding technique for PCM modems. Even more particularly, this invention relates to a novel trellis encoding technique which is based upon International Telecommunication Union (ITU) Standard V.34, which is incorporated herein by reference. The trellis encoding technique described in V.34 is based upon a trellis coding method and arrangement disclosed in U.S. Pat. No. 4,941,154, also incorporated herein by reference.

BACKGROUND OF THE INVENTION

[0003] The use of trellis encoding has provided substantial advantages in digital communication. The use of trellis encoding on the analog downstream channel of PCM modems should provide similar advantages. Unfortunately, the non-equal spacing of PCM symbols results in the errors being concentrated only in those symbols with small adjacent symbol spacing.

[0004] This unequal distribution of symbol errors per symbol spacing reduces the advantages of trellis encoding. The throughput loss of including trellis state information can be compensated by an increase of throughput due to the ability to communicate error-free in a higher noise environment. Also, the use of trellis encoding may not be compatible with the variety of transmit gain and spectral shaping proposed by others.

[0005] What is needed is a trellis encoding technique which uses a modified V.34 trellis encoding for use with the analog downstream of PCM modems.

SUMMARY OF THE INVENTION

[0006] A method of applying a multidimensional error reduction/correction algorithm on a stream of one dimensional symbols, comprising converting the stream of one dimensional symbols into a corresponding stream of two dimensional symbols; and, applying the multidimensional error reduction/correction algorithm to the stream of two dimensional symbols. The invention also provides a method of normalizing a metric used by an error reduction/correction algorithm on a stream of symbols wherein the symbols are non-uniformly spaced, comprising: determining a minimum distance (dmin) between two closest symbols in the stream, for each symbol in the stream, determining a minimum distance (dsym) between the each symbol in the stream and each of its adjacent neighboring symbols, and, normalizing the metric used by the error reduction/correction algorithm by the ratio dmin/dsym.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007]FIG. 1 illustrates an information processing system in a 1D trellis encoding device in accordance with an embodiment of the invention; and

[0008]FIG. 2 illustrates a process in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0009] This application discloses a modified V.34 trellis encoding for use with the analog downstream of PCM modems. In the description which follows, the symbol “D” is defined to mean “dimension” or “dimensional”. For example, “1D” means “one dimensional”, etc. The V.34 trellis encoding is modified for the following PCM enhancements:

[0010] A The 4D V.34 trellis encoding is modified for 1D symbols;

[0011] B. The input PCM symbol set is partitioned into four disjoint symbol sets;

[0012] C. The trellis decoder uses weighted error (metric) information; and

[0013] D. The use of a trellis encoder for any communication is optional.

[0014] Description of the 4D V.34 Trellis Encoder for 2D Symbols

[0015] The V.34 trellis encoder is constructed to operate on two 2D symbols. The process of trellis encoding is basically defined as follows: with m indicating each 4D period, n indicating each 2D period, and t being each 1D period being created respectively:

[0016] A. Generate the first trellis encoder input y(2m).

[0017] B. Calculate U₀(m) which is function of Y₀(m), V₀(m), and C₀(m).

[0018] C. Generate the second trellis encoder input y(2m+1) including the information encoded in U₀(m).

[0019] D. Map y(2m) and y(2m+1) to 2D subset labels s(2m) and s(2m+1) respectively.

[0020] E. Using s(2m) and s(2m+1), convert the subset labels to the four inputs Y₄(m), Y₃(m), Y₂(m), and Y₁(m).

[0021] F. Run the chosen systematic convolutional encoder (16 state, 32 state, 64 state) to generate Y₀(m+1).

[0022] Adaptation of the 4D V.34 Trellis Encoder for 1D Symbols

[0023] The adaptation to 1D symbols is simple. It is based upon the following observations:

[0024] A. The trellis encoding need not be 90 or even 180 degrees rotationally invariant. Thus, the analogous operation of U₀(m), which affects the rotation of the V.34 symbol, can now perform a transmit symbol subset selection.

[0025] B. The entire V.34 trellis encoding structure, namely the subsets labels s(2m), s(2m+1), Y₄(m), Y₃(m), Y₂(m), Y₁(m), and Y₀(m).

[0026] C. The V.34 trellis encoding structure is so constructed that the property: U₀(m) equals bit 0 of (s(2m) s(2m+1)) is always satisfied.

[0027] D. Each 1D symbol can be treated as one of the independent variables of the 2D symbol y(n), either as its real or imaginary component.

[0028] The adaptation of the 4D trellis encoder to 1D symbols requires generation of subset labels analogous to the 2D s(n) subset labels. Using the notation r(t) to represent the 1D subset labels, all possible y(t) symbols are assigned r(t) values such that adjacent (in amplitude) y symbols have the following assignments:

[0029] smaller y valu . . larger y values

[0030] . . . 00011011 . . .

[0031] These assignments create four subset partitions of the set of y symbol's created.

[0032] The mapping from r(t) values is then, from FIG. 9/V.34: TABLE 1 r(n), r(n + 1) to s(n) mapping r(n + 1) r(n) 00 01 10 11 11 001 110 101 010 10 100 011 000 111 01 101 010 001 110 00 000 111 100 011

[0033] An addition grouping of the four subsets of y are performed: those with r(t) values of 00,10, called the 0 grouping, and those with r(t) values of 01,11, called the 1 grouping.

[0034] The trellis encoding procedure is now:

[0035] A. Generate the first trellis encoder input and output symbol y(4m) selecting from any grouping. Map the symbol to its corresponding subset label r(4m).

[0036] B. Generate the second trellis encoder input and output symbol y(4m+1) selecting from any grouping. Map the symbol to its corresponding subset label r(4m+1).

[0037] C. Generate the third trellis encoder input and output symbol y(4m+2) selecting from any grouping. Map the symbol to its corresponding subset label r(4m+2).

[0038] D. Calculate the desired U₀(m) which is defined as:

[0039] R₀(m)=bit 0 (r(4m) ⊕r(4m+1)⊕r(4m+2)) U₀(m)=Y₀(m)⊕V₀(m)⊕R₀(m)

[0040] E. Generate the fourth trellis encoder input and output symbol y(4m+3). The symbol must come from the 0 grouping if U₀(m)=0 and from the 1 grouping if U₀(m)=1. Map the symbol to its corresponding subset label r(4m+3).

[0041] F. Using r(4m) and r(4m+1) to its respective s(2n) value. Using r(4m+2) and r(4m+3) to its respective s(2n+1) value.

[0042] G. Using s(2n) and s(2n+1), convert the subset labels to the four inputs Y₄(m), Y₃(m), Y₂(m), and Y₁(m).

[0043] Receiver Adaptation for PCM Encoding

[0044] The benefits of trellis encoding for PCM symbols can be further enhanced by scaling the metrics within the receiver. Normally, trellis encoding is used for communication systems with near equally spaced symbols for best performance over added white gaussian noise (AWGN) channels. The use of PCM codes result in symbols whose spacing is smaller for small and larger for large symbols. This results in an error on large symbols, which may be error-free without trellis encoding, to produce an error for smaller symbols.

[0045] The receiver can improve this problem. The smallest symbol spacing can be determined. This spacing, dmin, can be used to scale all other errors and hence metrics for differently spaced symbols. The scaling for any given symbol would become dmin/dsym where dsym is the spacing for a particular symbol.

[0046] This process results in large symbols contributing proportional rather than absolute information to the trellis decoding processes.

[0047] Trellis Coding Gain

[0048] The performance for equally spaced codes of the proposed trellis encoder is identical to that within V.34, approximately 4.5 dB. Unfortunately, the use of the proportionately spaced PCM codes results in less than this performance for low noise signals.

[0049] The proposed trellis encoder uses 1 bit every 4D symbol and costs 1/4 bit/symbol or 2000 bits/second to operate. For low noise receive signals, it only improves the performance of those few symbols with minimum receive spacing. If the additional codes allowed by the better S/N performance does not create more than an additional 1/4 bit/symbol in performance, the use of the trellis encoder is counter-productive.

[0050] For high noise receive signals, of course, the use of this trellis encoding will result in large throughput gains. Under noise representing throughput rates of 30 Kbps, the improvement can be over 4 KBps.

[0051] Because of this difference of performance of the use of trellis encoding for low and high noise PCM environments, the use of the trellis encoding should be optional. A receiver experiencing low noise can request no trellis encoding. A receiver experiencing high noise can. request whatever trellis encoding it implements.

[0052] In summary, this invention describes a practical method of adapting trellis encoding for the downstream signal on PCM modems. The trellis encoder described is simply the V.34 adapted for 1D symbols. It describes improvements the receiver can make to make the trellis decoding less sensitive to the proportionally spaced PCM coded symbols. It also describes the effect low and high noise signals has on the use of trellis encoding coding gain for PCM coded symbol.

[0053] The incorporation of trellis encoding has significant advantages for high noise signals and, as such, should be incorporated into the PCM modem specification. Because of its small benefits for low noise signals, though, the specification should allow the negotiation of no trellis encoding. The PCM receiver should determine the acceptability of using trellis encoding.

[0054] A recursive process in accordance with an embodiment of the invention is shown in FIG. 2, making reference to FIG. 1 which shows an information processing system in a 1D trellis encoding device in accordance with the foregoing description. In the process illustrated in FIG. 2, a transmit output is assigned (100) to a transmit symbol. Concurrently, a subset label is assigned (110) to the transmit symbol. N-1 subset labels are stored (120) for N-1 transmit symbols. Thus, an Nth transmit symbol is formed (130) such that an associated Nth subset label is partially determined by a combination of an output of an error reduction/correction algorithm and said N-1 stored subset labels. The transmit symbols and their assigned transmit outputs and subset labels are illustrated in FIG. 1.

[0055] These and other objects, features and advantages of the present invention will be readily apparent to those having ordinary skill in the art. For example, although a metric normalization method is described in the claims and based upon the determination of certain minimum distances between symbols in the stream, it will be appreciated that other normalization methods are also possible, based but not limited, for example, on signal level corresponding to amplitude or a function of amplitude. 

What is claimed is:
 1. A method of performing N-dimensional error reduction/correction on a stream of one dimensional transmit symbols, comprising: assigning a transmit output to a transmit symbol; concurrently assigning a subset label to said transmit symbol; storing N-1 subset labels for N-1 transmit symbols; and forming an Nth transmit symbol such that an associated Nth subset label is partially determined by a combination of an output of an error reduction/correction algorithm and said N-1 stored subset labels.
 2. The method recited in claim 1, wherein N-dimensional is 4 dimensional.
 3. The method recited in claim 1, wherein said error reduction/correction algorithm is performed by a trellis encoder.
 4. The method recited in claim 1, wherein said error reduction/correction algorithm is performed by a systematic convolutional encoder.
 5. The method recited in claim 1, wherein assigning to said transmit symbol a subset label comprises: ordering transmit outputs by value; and assigning subset labels to said transmit outputs in sequence.
 6. The method recited in claim 5, wherein ordering transmit outputs by value is performed according to increasing value of said transmit outputs.
 7. The method recited in claim 5, wherein assigning subset labels in sequence is performed according to ascending values of said subset labels.
 8. The method recited in claim 1, wherein forming said Nth transmit symbol further comprises: computing U₀ as a combination of a previous output of an error reduction/correction encoder performing said error reduction/correction algorithm and said N-1 stored subset labels; and forming said Nth transmit symbol such that a bit 0 of said associated Nth subset label is determined by U₀.
 9. The method recited in claim 8, wherein said error reduction/correction encoder is a trellis encoder.
 10. The method recited in claim 8, wherein a previous output of said error reduction/correction encoder is determined using said N-1 stored subset labels and said Nth subset label.
 11. The method recited in claim 8, wherein computing U₀ comprises determining a sum modulo 2 of said previous output of said error reduction/correction encoder and said N-1 stored subset labels.
 12. The method recited in claim 8, wherein said Nth transmit symbol is formed such that bit 0 of its associated Nth subset label is equal to U₀.
 13. The method recited in claim 8, wherein a previous output of said error reduction/correction encoder is determined by: mapping said N-1 stored subset labels and said Nth subset label to inputs of said error reduction/correction encoder; and calculating an output of said error reduction/correction encoder based on said inputs.
 14. The method recited in claim 8, wherein a previous output of said error reduction/correction encoder is determined by: mapping said N-1 stored subset labels and said Nth subset label to secondary subset labels; mapping said secondary subset labels to inputs of said error reduction/correction encoder; and calculating an output of said error reduction/correction encoder based on said inputs.
 15. The method recited in claim 8, wherein a previous output of said error reduction/correction encoder is determined by: mapping pairs of said N-1 stored subset labels and said Nth subset label to secondary subset labels; mapping said secondary subset labels to inputs of said error reduction/correction encoder, and; calculating an output of said error reduction/correction encoder based on said inputs.
 16. The method recited in claim 1, wherein forming said Nth transmit symbol further comprises: generating a verification sequence bit V₀; computing U₀ as a combination of a previous encoder output of an error reduction/correction encoder, said N-1 stored subset labels and a verification sequence bit V₀; and forming said Nth transmit symbol such that a bit 0 of its associated subset label is determined by U₀.
 17. A method of performing 4-dimensional error reduction/correction on a stream of one dimensional transmit symbols, comprising: assigning a transmit output to a transmit symbol; concurrently assigning a subset label to said transmit symbol, wherein transmit outputs are ordered by increasing value and subset labels are in ascending order; forming a first transmit symbol at a time 4m+0, where m is an integer, from input data and storing a subset label associated with said first transmit symbol as r(4m+0); forming a second transmit symbol at a time 4m+1 from input data and storing a subset label associated with the second transmit symbol as r(4m+1); forming a third transmit symbol at a time 4m+2 from input data and storing a subset label associated with the third transmit symbol as r(4m+2); computing U₀(m) as a sum modulo 2 of a previous output of a trellis encoder, Y₀(m) and said stored subset labels r(4m+0), r(4m+1) and r(4m+2), according to the equation U₀(m)=Y₀(m)⊕r(4m+0)⊕r(4m+1)⊕r(4m+2); forming a fourth transmit symbol at a time 4m+3 from input data and U₀(m) such that a bit 0 of a subset label r(4m+3) associated with the fourth transmit symbol is determined by U₀(m); mapping a pair of subset labels r(4m+0) and r(4m+1) to a secondary subset label s(2n+0) and further mapping a pair of subset labels r(4m+2) and r(4m+3) to a secondary subset label s(2n+1), where 2n=4m; mapping a pair of secondary subset labels s(2n+0) and s(2n+1) to inputs of said trellis encoder Y₁(m), Y₂(m), Y₃(m) and Y₄(m), and; calculating an output of said trellis encoder Y₀(m+1) from said input bits Y₁(m), Y₂(m), Y₃(m) and Y₄(m). 